Lesson 11 of 11 · 14 min
Chapter review
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Next Toppers - 12th ScienceWhole chapter · Hinglish
Displacement current to spectrum, quick revision
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Must-know facts
20 facts
- 01Displacement current id = ε₀ dΦE/dt; it produces a magnetic field exactly as a conduction current does.
- 02In a charging capacitor: ic = i in the wires, id = i in the gap; total current is continuous.
- 03Ampere-Maxwell law: ∮B·dl = μ₀ic + μ₀ε₀ dΦE/dt.
- 04Maxwell's four equations: Gauss (E), Gauss (B), Faraday, Ampere-Maxwell.
- 05∮B·dA = 0 because no magnetic monopoles are known.
- 06Accelerated charges radiate; charges at rest or in uniform motion do not.
- 07The frequency of the wave equals the frequency of the oscillating charge.
- 08Hertz produced and detected em waves in 1887; J. C. Bose produced waves of 25 mm to 5 mm.
- 09E, B and the direction of travel are mutually perpendicular; travel is along E × B.
- 10Ex = E₀ sin(kz − ωt), By = B₀ sin(kz − ωt): E and B in phase.
- 11c = 1/√(μ₀ε₀) ≈ 3 × 10⁸ m/s; ω = ck; νλ = c; B₀ = E₀/c.
- 12In a medium v = 1/√(με).
- 13em waves need no medium, and all of them travel at c in vacuum.
- 14Spectrum by decreasing wavelength: radio, microwave, infrared, visible, UV, X-rays, gamma.
- 15Visible: about 400-700 nm, 4 × 10¹⁴ to 7 × 10¹⁴ Hz.
- 16FM 88-108 MHz, AM 530-1710 kHz, TV 54-890 MHz.
- 17Microwaves: klystron, magnetron, Gunn diode; radar and ovens.
- 18Infrared = heat waves; used in remotes and physical therapy; causes the greenhouse effect.
- 19Ozone layer (40-50 km) absorbs most solar UV; glass absorbs UV.
- 20X-rays: electrons striking a metal target; gamma rays: radioactive nuclei.
Common traps
Where marks are lost
Formulas
6 to know
Displacement current
id = ε₀ dΦE/dt
Equals the conduction current in the leads of a charging capacitor.
Ampere-Maxwell law
∮B·dl = μ₀ic + μ₀ε₀ dΦE/dt
Total current i = ic + id.
Plane em wave
Ex = E₀ sin(kz − ωt), By = B₀ sin(kz − ωt)
k = 2π/λ, ω = 2πν.
Speed in vacuum
c = 1/√(μ₀ε₀) = ω/k = νλ
About 3 × 10⁸ m/s.
Field amplitudes
B₀ = E₀/c
E in V/m, B in T.
Speed in a medium
v = 1/√(με)
ε and μ of the medium.
Key terms
14 terms
- Conduction current
- Current carried by charges moving through a conductor.
- Displacement current
- ε₀ times the rate of change of electric flux; acts as a source of B like a real current.
- Ampere-Maxwell law
- Ampere's law with the displacement current added to the conduction current.
- Maxwell's equations
- The four laws of electromagnetism: Gauss's laws for E and B, Faraday's law and the Ampere-Maxwell law.
- Electromagnetic wave
- Coupled E and B fields oscillating at right angles to each other and to the direction of travel.
- Wave vector (k)
- Vector of size 2π/λ pointing along the direction of travel.
- Transverse wave
- A wave whose oscillations are perpendicular to the direction it travels.
- Electromagnetic spectrum
- The full range of em waves arranged by frequency or wavelength.
- Microwaves
- Short-wavelength radio waves in the GHz range, from 0.1 m to 1 mm.
- Infrared (heat waves)
- Waves from 1 mm to 700 nm that set molecules vibrating and so heat matter.
- Greenhouse effect
- Warming of the earth as CO₂ and water vapour trap the infrared the ground re-radiates.
- Ozone layer
- Layer about 40-50 km up that absorbs most of the sun's ultraviolet.
- Klystron, magnetron
- Vacuum tubes that generate microwaves.
- Gunn diode
- A solid-state source of microwaves.